The centrifuge is typically used for processing samples in the chemical, biological, and medical sciences when such samples need to be separated into at least two constituent components each having varying densities and/or sedimentary rates. A centrifuge is used to isolate particles in suspended state from the medium in which they are held. Many research and clinical applications rely on the isolation of cells, subcellular organelles, and macromolecules typically from samples that need to be individually processed.
A laboratory centrifuge fundamentally consists of a container, tube, or vial for holding a specimen or sample, the container, tube, or vial designed such that it is capable of withstanding the sizeable forces applied by the centrifuge; a sample holder such as, for example, a tub-shaped bowel, carousel, or bucket for holding a plurality of containers, tubes, or vials; a rotor that retains at least one sample holder; a shaft upon which the rotor is mounted; a motor for turning the shaft that simultaneously spins the rotor and the at least one sample holder rotatably attached thereto; optionally, a lid affixed to a centrifuge housing containing the sample holder, the rotor, the shaft, and the motor; and a motor speed controller for achieving a desired relative centrifugal force (RCF). Some centrifuges are also equipped with controllers that have conventionally been used to ensure the lid is properly affixed to the centrifuge housing, precisely employ a set time and RCF on a batch of samples, and to alert the operator the centrifuge is out of balance if the unit has been equipped with an imbalance detection system. The shaft is driven at an application dependent selected speed that can be as high as 10,000 revolutions-per-minute (RPM) or more.
The centrifuge subjects the samples to a centrifugal force. The amount of centrifugal force is directly proportional to the mass of the sample, the distance the sample is from the spin axis, and the angular velocity or spin rate squared. The effect of the applied centrifugal force is to impose a separation force on a sample that is typically orders of magnitude greater than gravity at the earth's surface, which causes the sample to separate into its multidensity components much more quickly and effectively than if not subjected to the added force.
There are two primary types of centrifugal separations—differential separation, which relies primarily on the size differences of suspended particles, and density gradient centrifugation, which is carried out in at least one layer of gradient medium added to the sample container. The cell medium in density gradient centrifugation may be selected to prefer distributions based on particle size, density, and any combination thereof. Further, there are multiple types of rotors that can typically be classified into three common categories—swinging bucket, fixed-angle, and vertical—each of which generally identifies the position of the sample tubes during rotation.
Certain analyses require precise centrifugation conditions. For example, a blood sample must be separated into its constituent parts—plasma and blood cells—for subsequent analysis. The degree of centrifugation imposed on a sample is termed RCF. RCF is proportional to the radius of the rotor and the square of the angular velocity or speed of the centrifuge, measured by RPM. The calculation for applied RCF may have to be adjusted depending on the type of rotor used in the centrifuge. The RCF measures how many times a unit of gravity, or “g-force”, is imposed on a processed sample. RCF is a ratio, in essence, of the applied centrifugal force relative to gravity.
Another parameter that is important to the overall degree of separation is the length of time a certain RCF is applied to a sample or also known as the total amount of force and time (F×T) or total FT that is applied to the sample. Failure to consistently apply the requisite RCF and centrifugation time to a particular sample can distort the final analysis of the separated material possibly rendering the results, for the most part, meaningless. Varying acceleration and deceleration profiles that contribute to the total FT can also impact the repeatability of results on separated samples.
Laboratory and/or clinical centrifugations conventionally are batch processes with most centrifuges designed to process multiple samples at once. When processing multiple, discrete samples, there is a delay in processing earlier samples placed into the centrifuge. This delay is known as dwell time. Furthermore, there must be sufficient samples available to fill the centrifuge or at least there must be enough samples to load the centrifuge in such a way that the centrifuge remains in balance about its rotational axis once centrifugation begins. The centrifuge may have static imbalances, dynamic imbalances, and any combination thereof. Static imbalances result from asymmetrical distributions of mass within the centrifuge. Dynamic imbalances may occur as variations in distribution of densities begin to occur throughout the samples that are being centrifuged. Operating a centrifuge that is not balanced can result in increased noise, incorrect final sample analysis because of the failure to achieve a requisite consistent RCF or because of possible sample resuspension as the rotation of the centrifuge moves through resonance peaks, and excessive vibration and machine movement possibly leading to damage or even full inoperability of the centrifuge unit. Further, batch centrifugation units are not amenable to efficiently processing critical specimens that arrive randomly but require quick turnaround analyses.
The extent of the idle time of a batch system capable of processing N samples but remaining idle until at least L samples are accumulated, with such samples arriving randomly to the batch system, has been addressed by Mathias A Dümmler and Alexander K. Schömig, “Using Discrete-Time Analysis in the Performance Evaluation of Manufacturing Systems” (paper presented at the annual International Conference on Semiconductor Manufacturing Operational Modeling and Simulation Meeting, San Francisco, Jan. 18-20, 1999). The amount of idle time is dependent upon both the number of samples, if any, remaining in the queue after the nth centrifugation starts and the number of samples arriving while the nth centrifugation is underway. The distribution of the number of samples remaining in the queue after the centrifugation has begun, yn(k), is given by:
            y      n        ⁡          (      k      )        =      {                                        0            ,                                                k            <                          n              -              1                                                                                                      ∑                                  i                  =                                      -                    ∞                                                                    n                  -                  1                                            ⁢                              max                ⁡                                  (                                      0                    ,                                                                                            x                                                      n                            -                            1                                                                          ⁡                                                  (                          i                          )                                                                    -                      K                                                        )                                                      ,                                                k            =                          n              -              1                                                                                      max              ⁡                              (                                  0                  ,                                                                                    x                                                  n                          -                          1                                                                    ⁡                                              (                        k                        )                                                              -                    K                                                  )                                      ,                                                k            >                          n              -              1.                                          where the probability distribution of all prior samples waiting to be processed as they have accumulated at the end of the last centrifugation, xn−1(k) is represented by:yn=max(0,xn−1−K)andK=L+min(max(0,xn−1−L),N−L).I.e., if the number of samples in the queue to be loaded just prior to the nth centrifugation is greater than the number of samples that can be loaded, then these samples will wait to be loaded in the next centrifugation sequence. If there are an insufficient number of samples to either fill the centrifuge or meet the minimum required number of samples to maintain balance in the centrifuge, then there will be idle time in the operation of the centrifuge until a sufficient additional number of samples become available for processing.
Assuming geometrically distributed arrival times, the distribution of the number of samples arriving during any nth period of operation of the centrifuge, γn(k), is given by:
            γ      n        ⁡          (      k      )        =            ∑              m        =        k            ∞        ⁢                  (                                            m                                                          k                                      )            ⁢                                    p            k                    ⁡                      (                          1              -              p                        )                                    m          -          k                    ⁢                        b          n                ⁡                  (          m          )                    where bn(m) is the distribution along the length of the nth centrifugation period and p is the probability of a sample arriving at any point in time.
The probability distribution of two random variables is given by the convolution theorem. Hence, the probability distribution for the number of samples waiting to be loaded after the nth centrifugation, xn(k), is given by:
            x      n        ⁡          (      k      )        =                              y          n                ⁡                  (          k          )                    ⊗                        γ          n                ⁡                  (          k          )                      =                  ∑                  l          =                      -            ∞                          ∞            ⁢                                    y            n                    ⁡                      (            l            )                          ·                                            γ              n                        ⁡                          (                              k                -                l                            )                                .                    I.e., the number of samples waiting to be loaded after the nth centrifugation for the next n+1th centrifugation is dependent on the number of samples remaining in the queue to be processed, if any, just prior to starting the nth centrifugation sequence and the number of samples that have arrived while the nth centrifugation is underway.
The mean time samples must wait before being centrifuged, W, is given by Little's law: W= Q| Rwhere Q is the mean number of samples in the queue at the start of centrifugation given by: Q=Σi·xn(i)and R is the average arrival rate of the samples.
Based on Little's formula, the mean waiting time of the samples before being centrifuged, W, is minimized when there are consistently no samples waiting to be processed at the start of any centrifugation as long as there are at least a sufficient number of samples, L, already loaded to maintain balance in the centrifuge.
The study provides revealing mathematical insight, using discrete time analysis, into the problems surrounding the potential limitations on batch processing in discrete time processing systems. As the analysis confirms, where the probability of appearance of a sample is reasonably consistent, then a centrifuge can be sized such that the idle time resulting from waiting for the requisite number of samples to arrive before centrifugation can begin can be minimized. Indeed, where such probabilities are known, the centrifuge can be sized such that there are a sufficient number of samples to fill the centrifuge without any idle time between each batch centrifugation sequence and any samples remaining at the end of a given period. However, such consistent probabilities in the clinical setting are rare. There will inevitably be variability in the probability of sample arrivals. Such variability typically is inconsistent and difficult to estimate. Hence, a centrifuge in the clinical setting typically needs to be sized for those periods when the probability of arrival of a sample is greatest in order to keep up with demand in those peak periods. Inevitably, this will lead to increased idle time when the probability of arrival of a sample is anything less than the maximum probability for which the centrifuge has been designed.
An alternative for laboratories that must process samples having varying probabilities of arrival of samples is to purchase additional centrifuges each having smaller capacities, but this comes at increased capital expenditure and operating costs. Even if a laboratory is willing to accept the increased costs for a multiple number of centrifuges, while idle time can be reduced, some amount of idle time will always remain as long as the probability for the arrival of a sample varies from the probabilities used in the design of the centrifuges.
Advancements have been made, for example, in the clinical laboratory to streamline sample processing and reduce the amount of sample that is needed on which to perform an analysis. The need to gain even further efficiency improvements from the centrifugation process has been recognized in the art. For example, U.S. Pat. No. 4,058,252 entitled “Automatic Sample Processing Apparatus” to Williams discloses advancing a number of centrifugation units each having a plurality of containers mounted on a conveyor to various processing stations. U.S. Pat. No. 6,060,022 entitled “Automated Sample Processing System Including Automatic Centrifuge Device” to Pang et al. discloses a centrifugation subsystem that involves loading containers to be processed in a plurality of buckets, checking that the buckets are in balance, loading the buckets into the centrifuge, centrifuging, and unloading the buckets from the centrifuge. However, these systems are limited since the sample holders must be balanced before they are placed in the centrifuge—a process that can prove to be time consuming. Centrifugation cannot begin until at least a minimum number of samples have been loaded such that the centrifugation units or buckets can maintain balance in the centrifuge. These batch processing systems will have idle times that can be determined by the discrete time analysis disclosed herein.
Automated loading and unloading procedures of samples by robotics are disclosed in, for example, U.S. Pat. No. 5,166,889 entitled “Robotic Liquid Sampling System” to Cloyd, U.S. Pat. No. 5,769,775 entitled “Automated Centrifuge for Automatically Receiving and Balancing Samples” to Quinlan, and U.S. Pat. No. 6,374,982 entitled “Robotics for Transporting Containers and Objects within an Automated Analytic Instrument and Service Tool for Servicing Robots” to Cohen et al. However, these automated processing techniques still require that some or all of the preliminary and subsequent sample processing steps be suspended or withheld until centrifugation is complete on the batch of samples being processed in the centrifuge.
Advances have also been made with respect to the need to balance centrifuges that process varying numbers of samples and samples that have varying amounts of a specimen to be processed. U.S. Pat. No. 5,769,775 to Quinlan discloses a method of determining an arrangement of a preselected number of sample racks each holding a plurality of containers with samples that are to be loaded in the centrifuge such that the unit will remain in balance in a given certain threshold. As further disclosed, the system may also have a weighing station for predetermining the proper weight distribution of the sample racks within the centrifuge, similar to the weighing station and plurality of buckets disclosed in U.S. Pat. No. 6,060,022. The methods that are the subject of these disclosures require that the centrifuge be balanced using a multitude of sample racks with a varying number of samples prior to centrifugation. The methodologies serve to potentially increase the idle time of the centrifuge depending on the extent of balancing and rebalancing of samples that is needed prior to loading the centrifuge with the sample racks or buckets.
Centrifuges can be manufactured to allow the unit to have more tolerance for off balance samples or even be self-balancing to some degree. For example, a centrifuge may have larger rotor bearings as disclosed in U.S. Pat. No. 5,769,775 or may have upper and lower bearing mounts that are capable of substantial movement in the horizontal plane for self-balancing as disclosed in U.S. Pat. No. 4,412,831 entitled “Two Plane Self-Balancing Centrifuge” to Avery et al. Conventionally, the self-balancing units seem to have been the less-favored approach since they increase the cost of the centrifuge, only serve to reduce the time for balancing samples prior to beginning centrifugation, and provide little, if any, efficiency gains during the batch centrifugation process. Such advantages have not been used to reduce the idle time of the centrifuge resulting from varying probabilities of arrival times of samples to be processed in the centrifuge.
A more automated system for controlling centrifuge balance is the subject of the disclosure in U.S. Pat. No. 6,635,007 entitled “Method and Apparatus for Detecting and Controlling Imbalance Conditions in a Centrifuge System” to Evans et al. A centrifuge imbalance is detected by an imbalance detection system that includes an accelerometer that measures longitudinal acceleration. When an imbalance is detected, a controller can automatically make adjustments to bring the centrifuge back into balance, though the disclosure is silent on what adjustments can be made. Admitting that centrifuge balancing is difficult to fully automate, U.S. Pat. No. 7,115,090 entitled “Method and Device for Pretreatment of Samples by Centrifuge” to Lagarde discloses a method that includes the steps of detecting the presence of tubes inside a container to be placed in the centrifuge, simulating the load of the centrifuge incorporating the container, selecting a suitable balancing container as needed, and removing the balancing container once centrifugation is complete.
While advancements have been made to streamline processing discrete samples in a centrifuge system and maintaining balance in the centrifuge system, there remains in the art a need to process a varying number of samples in a centrifuge while reducing, if not eliminating, the idle time of the unit resulting from the batch processing of samples. Further, the art requires that the centrifuge maintain balance about its rotational axis when processing such samples.
An additional need that remains in the art is the ability to process irregular critical samples that require priority handling without any substantial loss in efficiency of processing other discrete samples in the centrifuge system.